1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

Data from the speech features

1.2 The data set

TADPOLE_D1_D2 <- read.csv("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2.csv")
TADPOLE_D1_D2_Dict <- read.csv("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2_Dict.csv")
TADPOLE_D1_D2_Dict_LR <- as.data.frame(read_excel("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2_Dict_LR.xlsx",sheet = "LeftRightFeatures"))


rownames(TADPOLE_D1_D2_Dict) <- TADPOLE_D1_D2_Dict$FLDNAME

1.3 Conditioning the data


# mm3 to mm
isVolume <- c("Ventricles","Hippocampus","WholeBrain","Entorhinal","Fusiform","MidTemp","ICV",
              TADPOLE_D1_D2_Dict$FLDNAME[str_detect(TADPOLE_D1_D2_Dict$TEXT,"Volume")]
              )


#TADPOLE_D1_D2[,isVolume] <- apply(TADPOLE_D1_D2[,isVolume],2,'^',(1/3))
TADPOLE_D1_D2[,isVolume] <- TADPOLE_D1_D2[,isVolume]^(1/3)

# mm2 to mm
isArea <- TADPOLE_D1_D2_Dict$FLDNAME[str_detect(TADPOLE_D1_D2_Dict$TEXT,"Area")]
TADPOLE_D1_D2[,isArea] <- sqrt(TADPOLE_D1_D2[,isArea])

# Get only cross sectional measurements
FreeSurfersetCross <- str_detect(colnames(TADPOLE_D1_D2),"UCSFFSX")

# The subset of baseline measurements
baselineTadpole <- subset(TADPOLE_D1_D2,VISCODE=="bl")
table(baselineTadpole$DX)
                   Dementia Dementia to MCI             MCI MCI to Dementia 
          7             336               1             864               5 
  MCI to NL              NL       NL to MCI 
          2             521               1 
table(baselineTadpole$DX_bl)

AD CN EMCI LMCI SMC 342 417 310 562 106


rownames(baselineTadpole) <- baselineTadpole$PTID


validBaselineTadpole <- cbind(DX=baselineTadpole$DX_bl,
                                 AGE=baselineTadpole$AGE,
                                 Gender=1*(baselineTadpole$PTGENDER=="Female"),
                                 ADAS11=baselineTadpole$ADAS11,
                                 ADAS13=baselineTadpole$ADAS13,
                                 MMSE=baselineTadpole$MMSE,
                                 RAVLT_immediate=baselineTadpole$RAVLT_immediate,
                                 RAVLT_learning=baselineTadpole$RAVLT_learning,
                                 RAVLT_forgetting=baselineTadpole$RAVLT_forgetting,
                                 RAVLT_perc_forgetting=baselineTadpole$RAVLT_perc_forgetting,
                                 FAQ=baselineTadpole$FAQ,
                                 Ventricles=baselineTadpole$Ventricles,
                                 Hippocampus=baselineTadpole$Hippocampus,
                                 WholeBrain=baselineTadpole$WholeBrain,
                                 Entorhinal=baselineTadpole$Entorhinal,
                                 Fusiform=baselineTadpole$Fusiform,
                                 MidTemp=baselineTadpole$MidTemp,
                                 ICV=baselineTadpole$ICV,
                                 baselineTadpole[,FreeSurfersetCross])


LeftFields <- TADPOLE_D1_D2_Dict_LR$LFN
names(LeftFields) <- LeftFields
LeftFields <- LeftFields[LeftFields %in% colnames(validBaselineTadpole)]
RightFields <- TADPOLE_D1_D2_Dict_LR$RFN
names(RightFields) <- RightFields
RightFields <- RightFields[RightFields %in% colnames(validBaselineTadpole)]

## Normalize to ICV
validBaselineTadpole$Ventricles=validBaselineTadpole$Ventricles/validBaselineTadpole$ICV
validBaselineTadpole$Hippocampus=validBaselineTadpole$Hippocampus/validBaselineTadpole$ICV
validBaselineTadpole$WholeBrain=validBaselineTadpole$WholeBrain/validBaselineTadpole$ICV
validBaselineTadpole$Entorhinal=validBaselineTadpole$Entorhinal/validBaselineTadpole$ICV
validBaselineTadpole$Fusiform=validBaselineTadpole$Fusiform/validBaselineTadpole$ICV
validBaselineTadpole$MidTemp=validBaselineTadpole$MidTemp/validBaselineTadpole$ICV

leftData <- validBaselineTadpole[,LeftFields]/validBaselineTadpole$ICV
RightData <- validBaselineTadpole[,RightFields]/validBaselineTadpole$ICV

## get mean and relative difference 
meanLeftRight <- (leftData + RightData)/2
difLeftRight <- abs(leftData - RightData)
reldifLeftRight <- difLeftRight/meanLeftRight
colnames(meanLeftRight) <- paste("M",colnames(meanLeftRight),sep="_")
colnames(difLeftRight) <- paste("D",colnames(difLeftRight),sep="_")
colnames(reldifLeftRight) <- paste("RD",colnames(reldifLeftRight),sep="_")


validBaselineTadpole <- validBaselineTadpole[,!(colnames(validBaselineTadpole) %in% 
                                               c(LeftFields,RightFields))]
validBaselineTadpole <- cbind(validBaselineTadpole,meanLeftRight,difLeftRight,reldifLeftRight)
#validBaselineTadpole <- cbind(validBaselineTadpole,meanLeftRight,difLeftRight)
#validBaselineTadpole <- cbind(validBaselineTadpole,leftData,RightData)

## Remove columns with too many NA more than %15 of NA
nacount <- apply(is.na(validBaselineTadpole),2,sum)/nrow(validBaselineTadpole) < 0.15
diagnose <- validBaselineTadpole$DX
pander::pander(table(diagnose))
AD CN EMCI LMCI SMC
342 417 310 562 106
validBaselineTadpole <- validBaselineTadpole[,nacount]
## Remove character columns
ischar <- sapply(validBaselineTadpole,class) == "character"
validBaselineTadpole <- validBaselineTadpole[,!ischar]
## Place back diagnose
validBaselineTadpole$DX <- diagnose


validBaselineTadpole <- validBaselineTadpole[complete.cases(validBaselineTadpole),]
ischar <- sapply(validBaselineTadpole,class) == "character"
validBaselineTadpole[,!ischar] <- sapply(validBaselineTadpole[,!ischar],as.numeric)

colnames(validBaselineTadpole) <- str_remove_all(colnames(validBaselineTadpole),"_UCSFFSX_11_02_15_UCSFFSX51_08_01_16")
colnames(validBaselineTadpole) <- str_replace_all(colnames(validBaselineTadpole)," ","_")
validBaselineTadpole$LONISID <- NULL
validBaselineTadpole$IMAGEUID <- NULL
validBaselineTadpole$LONIUID <- NULL

diagnose <- as.character(validBaselineTadpole$DX)
validBaselineTadpole$DX <- diagnose
pander::pander(table(validBaselineTadpole$DX))
AD CN EMCI LMCI SMC
245 359 272 444 93


validBaselineTadpole[validBaselineTadpole$DX %in% c("EMCI","LMCI"),"DX"] <- "MCI" 
validBaselineTadpole[validBaselineTadpole$DX %in% c("CN","SMC"),"DX"] <- "NL" 

pander::pander(table(validBaselineTadpole$DX))
AD MCI NL
245 716 452

1.4 Get the Time To Event on MCI Subjects


subjectsID <- rownames(validBaselineTadpole)
visitsID <- unique(TADPOLE_D1_D2$VISCODE)
baseDx <- TADPOLE_D1_D2[TADPOLE_D1_D2$VISCODE=="bl",c("PTID","DX","EXAMDATE")]
rownames(baseDx) <- baseDx$PTID 
baseDx <- baseDx[subjectsID,]
lastDx <- baseDx
toDementia <- baseDx
table(lastDx$DX)
   Dementia Dementia to MCI             MCI MCI to Dementia       MCI to NL 
        244               1             711               2               2 
         NL       NL to MCI 
        452               1 
hasDementia <- lastDx$PTID[str_detect(lastDx$DX,"Dementia")]


for (vid in visitsID)
{
  DxValue <- TADPOLE_D1_D2[TADPOLE_D1_D2$VISCODE==vid,c("PTID","DX","EXAMDATE")]
  rownames(DxValue) <- DxValue$PTID 
  DxValue <- DxValue[DxValue$PTID %in% subjectsID,]
  noDX <- DxValue$PTID[nchar(DxValue$DX) < 1]
  print(length(noDX))
  DxValue[noDX,] <- lastDx[noDX,]
  inLast <- lastDx$PTID[lastDx$PTID %in% DxValue$PTID]
  print(length(inLast))
  lastDx[inLast,] <- DxValue[inLast,]
  noDementia <- !(toDementia$PTID %in% hasDementia)
  toDementia[noDementia,] <- lastDx[noDementia,]
  hasDementia <- unique(c(hasDementia,lastDx$PTID[str_detect(lastDx$DX,"Dementia")]))
}

[1] 0 [1] 1413 [1] 2 [1] 1326 [1] 6 [1] 1218 [1] 23 [1] 1095 [1] 805 [1] 1058 [1] 29 [1] 710 [1] 20 [1] 212 [1] 14 [1] 167 [1] 32 [1] 553 [1] 25 [1] 298 [1] 18 [1] 130 [1] 667 [1] 667 [1] 112 [1] 112 [1] 176 [1] 176 [1] 177 [1] 177 [1] 625 [1] 625 [1] 251 [1] 251 [1] 159 [1] 159 [1] 7 [1] 7 [1] 17 [1] 99 [1] 9 [1] 63 [1] 1 [1] 1

table(lastDx$DX)
   Dementia Dementia to MCI             MCI MCI to Dementia       MCI to NL 
        428               2             463              80               7 
         NL  NL to Dementia       NL to MCI 
        406               1              26 
baseMCI <-baseDx$PTID[baseDx$DX == "MCI"]
lastDementia <- lastDx$PTID[str_detect(lastDx$DX,"Dementia")]
lastDementia2 <- toDementia$PTID[str_detect(toDementia$DX,"Dementia")]
lastNL <- lastDx$PTID[str_detect(lastDx$DX,"NL")]

MCIatBaseline <- baseDx[baseMCI,]
MCIatEvent <- toDementia[baseMCI,]
MCIatLast <- lastDx[baseMCI,]

MCIconverters <- MCIatBaseline[baseMCI %in% lastDementia,]
MCI_No_converters <- MCIatBaseline[!(baseMCI %in% MCIconverters$PTID),]
MCIconverters$TimeToEvent <- (as.Date(toDementia[MCIconverters$PTID,"EXAMDATE"]) 
                                   - as.Date(MCIconverters$EXAMDATE))

sum(MCIconverters$TimeToEvent ==0)

[1] 0



MCIconverters$AtEventDX <- MCIatEvent[MCIconverters$PTID,"DX"]
MCIconverters$LastDX <- MCIatLast[MCIconverters$PTID,"DX"]

MCI_No_converters$TimeToEvent <- (as.Date(lastDx[MCI_No_converters$PTID,"EXAMDATE"]) 
                                   - as.Date(MCI_No_converters$EXAMDATE))

MCI_No_converters$LastDX <- MCIatLast[MCI_No_converters$PTID,"DX"]

MCI_No_converters <- subset(MCI_No_converters,TimeToEvent > 0)

2 Prognosis MCI to AD Conversion

2.1 the set


MCIPrognosisIDs <- c(MCIconverters$PTID,MCI_No_converters$PTID)

TADPOLECrossMRI <- validBaselineTadpole[MCIPrognosisIDs,]
table(TADPOLECrossMRI$DX)

MCI 680

TADPOLECrossMRI$DX <- NULL
TADPOLECrossMRI$status <- 1*(rownames(TADPOLECrossMRI) %in% MCIconverters$PTID)
table(TADPOLECrossMRI$status)

0 1 436 244

2.1.0.1 Standarize the names for the reporting

studyName <- "TADPOLE"
dataframe <- TADPOLECrossMRI
outcome <- "status"

TopVariables <- 10

thro <- 0.60
cexheat = 0.15

2.2 Generaring the report

2.2.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

2.2.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))
rows col
680 477
pander::pander(table(dataframe[,outcome]))
0 1
436 244

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

2.2.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns


  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

2.3 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

2.3.0.1 Correlation Matrix of the Data

The heat map of the data


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9996707

2.4 The decorrelation


DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  ICV D_ST17SV RD_ST56CV D_ST65SV D_ST61SV D_ST36CV 
#>             AGE          ADAS11          ADAS13            MMSE RAVLT_immediate 
#>      0.02521008      0.35924370      0.36134454      0.01890756      0.11344538 
#>  RAVLT_learning 
#>      0.07773109 
#> 
#>  Included: 476 , Uni p: 0.0003151261 , Base Size: 56 , Rcrit: 0.1307612 
#> 
#> 
 1 <R=0.918,thr=0.950>, Top: 153< 1 >.[Fa= 153 ]( 153 , 153 , 0 ),<|><>Tot Used: 306 , Added: 153 , Zero Std: 0 , Max Cor: 0.909
#> 
 2 <R=0.778,thr=0.900>, Top: 3< 1 >[Fa= 156 ]( 3 , 3 , 153 ),<|><>Tot Used: 312 , Added: 3 , Zero Std: 0 , Max Cor: 0.884
#> 
 3 <R=0.776,thr=0.800>, Top: 41< 1 >[Fa= 188 ]( 39 , 49 , 156 ),<|><>Tot Used: 359 , Added: 49 , Zero Std: 0 , Max Cor: 0.923
#> 
 4 <R=0.747,thr=0.900>, Top: 1< 1 >[Fa= 189 ]( 1 , 1 , 188 ),<|><>Tot Used: 360 , Added: 1 , Zero Std: 0 , Max Cor: 0.841
#> 
 5 <R=0.746,thr=0.800>, Top: 1< 1 >[Fa= 190 ]( 1 , 1 , 189 ),<|><>Tot Used: 362 , Added: 1 , Zero Std: 0 , Max Cor: 0.800
#> 
 6 <R=0.745,thr=0.700>, Top: 114< 1 >.[Fa= 275 ]( 112 , 120 , 190 ),<|><>Tot Used: 451 , Added: 120 , Zero Std: 0 , Max Cor: 0.748
#> 
 7 <R=0.656,thr=0.700>, Top: 1< 1 >[Fa= 276 ]( 1 , 1 , 275 ),<|><>Tot Used: 453 , Added: 1 , Zero Std: 0 , Max Cor: 0.696
#> 
 8 <R=0.654,thr=0.600>, Top: 44< 1 >[Fa= 292 ]( 43 , 59 , 276 ),<|><>Tot Used: 468 , Added: 59 , Zero Std: 0 , Max Cor: 0.680
#> 
 9 <R=0.640,thr=0.600>, Top: 3< 1 >[Fa= 294 ]( 3 , 3 , 292 ),<|><>Tot Used: 468 , Added: 3 , Zero Std: 0 , Max Cor: 0.746
#> 
 10 <R=0.746,thr=0.700>, Top: 1< 1 >[Fa= 295 ]( 1 , 1 , 294 ),<|><>Tot Used: 468 , Added: 1 , Zero Std: 0 , Max Cor: 0.599
#> 
 11 <R=0.599,thr=0.600>
#> 
 [ 11 ], 0.5988799 Decor Dimension: 468 Nused: 468 . Cor to Base: 305 , ABase: 476 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

1378

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

1286

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

0.827

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.664


varratio <- attr(DEdataframe,"VarRatio")

pander::pander(tail(varratio))
La_RD_ST61SV La_RD_ST65SV La_RD_ST17SV La_RD_ST52CV La_RD_ST129CV La_ST10CV
0.00369 0.00358 0.00274 0.00272 0.00226 0.000658

2.4.1 The decorrelation matrix


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
  
  
  
}

2.4.2 Formulas Network

Displaying the features associations

par(op)
clustable <- c("To many variables")


  transform <- attr(DEdataframe,"UPLTM") != 0
  tnames <- colnames(transform)
  colnames(transform) <- str_remove_all(colnames(transform),"La_")
  transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
  
  
  fscore <- attr(DEdataframe,"fscore")
  VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
  names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
  VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization

  VertexSize <- VertexSize[rownames(transform)]
  rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  
  ntop <- min(10,length(rsum))


  topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
  rtrans <- transform[topfeatures,]
  csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
  rtrans <- rtrans[,csum]
  topfeatures <- unique(c(topfeatures,colnames(rtrans)))
  print(ncol(transform))

[1] 468

  transform <- transform[topfeatures,topfeatures]
  print(ncol(transform))

[1] 89

  if (ncol(transform)>100)
  {
    csum <- apply(1*(transform !=0),1,sum) 
    csum <- csum[csum > 1]
    csum <- csum + 0.01*VertexSize[names(csum)]
    csum <- csum[order(-csum)]
    tpsum <- min(20,length(csum))
    trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
    rtrans <- transform[trsum,]
    topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
    transform <- transform[topfeatures,topfeatures]
    if (nrow(transform) > 150)
    {
      csum <- apply(1*(rtrans != 0 ),2,sum)
      csum <- csum + 0.01*VertexSize[names(csum)]
      csum <- csum[order(-csum)]
      tpsum <- min(130,length(csum))
      csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
      csum <- unique(c(trsum,csum))
      transform <- transform[csum,csum]
    }
    print(ncol(transform))
  }

    if (ncol(transform) < 150)
    {

      gplots::heatmap.2(transform,
                        trace = "none",
                        mar = c(5,5),
                        col=rev(heat.colors(5)),
                        main = "Red Decorrelation matrix",
                        cexRow = cexheat,
                        cexCol = cexheat,
                       srtCol=45,
                       srtRow=45,
                        key.title=NA,
                        key.xlab="|Beta|>0",
                        xlab="Output Feature", ylab="Input Feature")
  
      par(op)
      VertexSize <- VertexSize[colnames(transform)]
      gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
      gr$layout <- layout_with_fr
      
#      fc <- cluster_optimal(gr)
        fc <- cluster_walktrap (gr,steps=50)
      plot(fc, gr,
           edge.width = 2*E(gr)$weight,
           vertex.size=VertexSize,
           edge.arrow.size=0.5,
           edge.arrow.width=0.5,
           vertex.label.cex=(0.15+0.05*VertexSize),
           vertex.label.dist=0.5 + 0.05*VertexSize,
           main="Top Feature Association")
      
      varratios <- varratio
      fscores <- fscore
      names(varratios) <- str_remove_all(names(varratios),"La_")
      names(fscores) <- str_remove_all(names(fscores),"La_")

      dc <- getLatentCoefficients(DEdataframe)
      theCharformulas <- attr(dc,"LatentCharFormulas")

      
      clustable <- as.data.frame(cbind(Variable=fc$names,
                                       Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
                                       Class=fc$membership,
                                       ResidualVariance=round(varratios[fc$names],3),
                                       Fscore=round(fscores[fc$names],3)
                                       )
                                 )
      rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
      clustable$Variable <- NULL
      clustable$Class <- as.integer(clustable$Class)
      clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
      clustable$Fscore <- as.numeric(clustable$Fscore)
      clustable <- clustable[order(-clustable$Fscore),]
      clustable <- clustable[order(clustable$Class),]
      clustable <- clustable[clustable$Fscore >= -1,]
      topv <- min(50,nrow(clustable))
      clustable <- clustable[1:topv,]
    }


pander::pander(clustable)
  Formula Class ResidualVariance Fscore
D_ST47CV NA 1 1.000 2
RD_ST47CV - (7.852)D_ST47CV + RD_ST47CV 1 0.011 1
M_ST47CV + M_ST47CV - (9.554)D_ST47CV + (1.217)RD_ST47CV 1 0.333 0
RD_ST47SA - (9.092)D_ST47CV + RD_ST47SA 1 0.271 0
D_ST47SA + D_ST47SA - (2.743)D_ST47CV - (0.307)RD_ST47SA + (0.349)RD_ST47CV 1 0.006 -1
D_ST34CV NA 2 1.000 2
RD_ST34CV - (8.906)D_ST34CV + RD_ST34CV 2 0.009 1
M_ST34CV + M_ST34CV - (13.746)D_ST34CV + (1.544)RD_ST34CV 2 0.352 0
RD_ST34SA - (8.537)D_ST34CV + RD_ST34SA 2 0.515 0
D_ST34SA + D_ST34SA - (2.504)D_ST34CV - (0.259)RD_ST34SA + (0.281)RD_ST34CV 2 0.007 -1
D_ST15CV NA 3 1.000 2
RD_ST15CV - (6.775)D_ST15CV + RD_ST15CV 3 0.008 1
M_ST15CV + M_ST15CV - (13.253)D_ST15CV + (1.956)RD_ST15CV 3 0.363 0
RD_ST15SA - (7.869)D_ST15CV + RD_ST15SA 3 0.318 0
D_ST15SA + D_ST15SA - (2.919)D_ST15CV - (0.390)RD_ST15SA + (0.431)RD_ST15CV 3 0.006 -1
M_ST59TA NA 4 1.000 29
M_ST129CV - (2.509)M_ST59TA + M_ST129CV 4 0.614 2
M_ST32TA + M_ST32TA - (0.812)M_ST59TA 4 0.422 1
M_ST48TA + M_ST48TA - (0.457)M_ST59TA 4 0.570 1
M_ST52TA + M_ST52TA - (0.828)M_ST59TA 4 0.276 0
M_ST56TA + M_ST56TA - (0.792)M_ST59TA 4 0.318 0
M_ST13TA + M_ST13TA - (0.882)M_ST59TA 4 0.317 -1
M_ST15TA + M_ST15TA - (0.839)M_ST59TA 4 0.273 -1
M_ST31TA + M_ST31TA - (0.930)M_ST59TA 4 0.174 -1
M_ST45TA + M_ST45TA - (0.755)M_ST59TA 4 0.296 -1
M_ST47TA + M_ST47TA - (0.736)M_ST59TA 4 0.375 -1
M_ST49TA + M_ST49TA - (0.719)M_ST59TA 4 0.303 -1
M_ST51TA + M_ST51TA - (0.995)M_ST59TA 4 0.295 -1
M_ST58TA + M_ST58TA - (0.918)M_ST59TA 4 0.315 -1
RD_ST43TA + (2.424)M_ST59TA - (54.888)D_ST43TA + RD_ST43TA 4 0.019 -1
D_ST54CV NA 5 1.000 2
RD_ST54CV - (9.266)D_ST54CV + RD_ST54CV 5 0.013 1
M_ST54CV + M_ST54CV - (7.520)D_ST54CV + (0.812)RD_ST54CV 5 0.332 0
RD_ST54SA - (9.981)D_ST54CV + RD_ST54SA 5 0.413 0
D_ST54SA + D_ST54SA - (3.032)D_ST54CV - (0.215)RD_ST54SA + (0.327)RD_ST54CV 5 0.012 -1
D_ST32CV NA 6 1.000 2
RD_ST32CV - (5.670)D_ST32CV + RD_ST32CV 6 0.008 1
M_ST32CV + M_ST32CV - (12.354)D_ST32CV + (2.179)RD_ST32CV 6 0.484 0
RD_ST32SA - (5.230)D_ST32CV + RD_ST32SA 6 0.495 0
D_ST32SA + D_ST32SA - (2.287)D_ST32CV - (0.464)RD_ST32SA + (0.403)RD_ST32CV 6 0.005 -1
D_ST45CV NA 7 1.000 2
RD_ST45CV - (7.280)D_ST45CV + RD_ST45CV 7 0.008 2
RD_ST45SA - (9.378)D_ST45CV + RD_ST45SA 7 0.228 0
M_ST45SA + M_ST45SA - (4.835)D_ST45SA - (5.514)D_ST45CV + (1.640)RD_ST45SA + (0.757)RD_ST45CV 7 0.370 -1
D_ST45SA + D_ST45SA - (3.414)D_ST45CV - (0.339)RD_ST45SA + (0.469)RD_ST45CV 7 0.007 -1
M_ST37SV NA 8 1.000 5
Ventricles + Ventricles - (1.275)M_ST37SV 8 0.013 -1
ST127SV + ST127SV - (29.897)M_ST37SV 8 0.441 -1
ST7SV + ST7SV - (18.157)M_ST37SV 8 0.550 -1
RD_ST30SV + (0.642)M_ST37SV - (12.479)D_ST30SV + RD_ST30SV 8 0.110 -1

par(op)

2.5 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

2.6 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after ILAA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.5988799

2.7 U-MAP Visualization of features

2.7.1 The UMAP on Raw Data


  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  topvars <- univariate_BinEnsemble(dataframe,outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

ADAS11, ADAS13, RAVLT_immediate, FAQ, Hippocampus and WholeBrain

#  names(topvars)
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])

#}

2.7.2 The decorralted UMAP

  varlistcV <- names(varratio[varratio >= 0.01])
  topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

FAQ, ADAS13, M_ST29SV, RAVLT_perc_forgetting, La_D_ST31CV and RAVLT_learning


  varlistcV <- varlistcV[varlistcV != outcome]
  
#  DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])

#}

2.8 Univariate Analysis

2.8.1 Univariate



univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : M_ST24SA 200 : D_ST49TA 300 : D_ST47CV 400 : RD_ST24SA




univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_M_ST24SA 200 : D_ST49TA 300 : D_ST47CV 400 : La_RD_ST24SA

2.8.2 Final Table


univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
ADAS13 20.7611 6.16923 14.0091 5.78970 0.03549 0.788
ADAS11 12.8635 4.56128 8.7155 3.84978 0.00264 0.761
FAQ 5.4631 4.90262 1.9266 2.98257 0.00000 0.756
M_ST40CV 0.1799 0.00875 0.1875 0.00763 0.28199 0.750
M_ST29SV 0.1253 0.00708 0.1321 0.00750 0.58088 0.745
M_ST12SV 0.0913 0.00535 0.0962 0.00550 0.50030 0.744
Hippocampus 0.1582 0.00886 0.1664 0.00945 0.44340 0.737
RAVLT_immediate 29.0205 7.69236 37.2798 10.92838 0.04406 0.728
M_ST24CV 0.0996 0.00800 0.1059 0.00706 0.04673 0.727
M_ST31CV 0.1910 0.00945 0.1986 0.00902 0.94566 0.717


topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
ADAS13 20.761066 6.17e+00 14.009106 5.79e+00 3.55e-02 0.788
FAQ 5.463115 4.90e+00 1.926606 2.98e+00 0.00e+00 0.756
M_ST29SV 0.125302 7.08e-03 0.132097 7.50e-03 5.81e-01 0.745
La_RD_ST40CV 0.000721 3.70e-03 -0.001552 2.58e-03 2.53e-06 0.718
RAVLT_perc_forgetting 74.353614 2.92e+01 52.421164 3.14e+01 1.42e-03 0.700
La_RD_ST12SV 0.000499 3.05e-03 -0.001192 3.04e-03 1.28e-12 0.697
La_D_ST31CV -0.000036 8.45e-04 0.000474 7.12e-04 1.64e-02 0.696
La_M_ST24CV 0.100098 5.62e-03 0.103429 4.96e-03 1.78e-01 0.691
La_RD_ST26CV 0.000512 2.25e-03 -0.000811 2.08e-03 1.64e-07 0.690
La_RD_ST58CV 0.000413 2.10e-03 -0.000648 1.46e-03 2.45e-06 0.687

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))
mean total fraction
2.64 337 0.706

theCharformulas <- attr(dc,"LatentCharFormulas")

topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])
  DecorFormula caseMean caseStd controlMean controlStd controlKSP ROCAUC RAWAUC fscores varratio
ADAS13 NA 20.761066 6.17e+00 14.009106 5.79e+00 3.55e-02 0.788 0.788 2 1.00000
ADAS11 NA 12.863525 4.56e+00 8.715528 3.85e+00 2.64e-03 0.761 0.761 NA NA
FAQ NA 5.463115 4.90e+00 1.926606 2.98e+00 0.00e+00 0.756 0.756 0 1.00000
M_ST40CV NA 0.179856 8.75e-03 0.187527 7.63e-03 2.82e-01 0.750 0.750 NA NA
M_ST29SV NA 0.125302 7.08e-03 0.132097 7.50e-03 5.81e-01 0.745 0.745 6 1.00000
M_ST12SV NA 0.091327 5.35e-03 0.096219 5.50e-03 5.00e-01 0.744 0.744 NA NA
Hippocampus NA 0.158226 8.86e-03 0.166444 9.45e-03 4.43e-01 0.737 0.737 NA NA
RAVLT_immediate NA 29.020492 7.69e+00 37.279817 1.09e+01 4.41e-02 0.728 0.728 NA NA
M_ST24CV NA 0.099630 8.00e-03 0.105940 7.06e-03 4.67e-02 0.727 0.727 NA NA
La_RD_ST40CV - (5.536)D_ST40CV + RD_ST40CV 0.000721 3.70e-03 -0.001552 2.58e-03 2.53e-06 0.718 0.585 1 0.00851
M_ST31CV NA 0.191026 9.45e-03 0.198568 9.02e-03 9.46e-01 0.717 0.717 NA NA
RAVLT_perc_forgetting NA 74.353614 2.92e+01 52.421164 3.14e+01 1.42e-03 0.700 0.700 1 1.00000
La_RD_ST12SV - (10.875)D_ST12SV + RD_ST12SV 0.000499 3.05e-03 -0.001192 3.04e-03 1.28e-12 0.697 0.552 -1 0.01050
La_D_ST31CV + D_ST31CV - (0.191)RD_ST31CV -0.000036 8.45e-04 0.000474 7.12e-04 1.64e-02 0.696 0.511 1 0.01070
La_M_ST24CV + M_ST24CV - (8.320)D_ST24CV + (0.827)RD_ST24CV 0.100098 5.62e-03 0.103429 4.96e-03 1.78e-01 0.691 0.727 -1 0.46302
La_RD_ST26CV - (5.692)D_ST26CV + RD_ST26CV 0.000512 2.25e-03 -0.000811 2.08e-03 1.64e-07 0.690 0.534 0 0.00632
La_RD_ST58CV - (5.448)D_ST58CV + RD_ST58CV 0.000413 2.10e-03 -0.000648 1.46e-03 2.45e-06 0.687 0.554 1 0.00596

2.9 Comparing ILAA vs PCA vs EFA

2.9.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

2.9.2 EFA


EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

2.10 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }


pander::pander(table(dataframe[,outcome],pr))
  0 1
0 330 106
1 36 208
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.791 0.759 0.821
3 se 0.852 0.802 0.894
4 sp 0.757 0.714 0.796
6 diag.or 17.987 11.866 27.267

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))
  0 1
0 396 40
1 109 135
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.781 0.748 0.811
3 se 0.553 0.489 0.617
4 sp 0.908 0.877 0.934
6 diag.or 12.261 8.124 18.506

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))
  0 1
0 399 37
1 135 109
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.747 0.713 0.779
3 se 0.447 0.383 0.511
4 sp 0.915 0.885 0.940
6 diag.or 8.707 5.716 13.263


par(op)

2.10.1 EFA


  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }


  pander::pander(table(EFAdataframe[,outcome],pr))
  0 1
0 365 71
1 77 167
  pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.782 0.749 0.813
3 se 0.684 0.622 0.742
4 sp 0.837 0.799 0.871
6 diag.or 11.150 7.695 16.155
  par(op)